Fard

Yes, your Wudu is valid if you do the obligatory actions only and skip the recommended actions.

You can refer to Al0Fiqh A'lal Mathahib Al-Khamsah.

Wassalam. 

If there was an understanding between them that he spends on her more than the basic needs of food and clothes and shelter and she looks after the household matters, such understanding makes it compulsory on both of them to full fil that mutual understanding. Some people say that wife has no responsibility at all at home more than matrimonial matters for her husband, but many scholars say that the understood agreement on her responsibilities at home matters and must be obliged.

Wassalam.

Fajr Prayer time is between Fajr time and sunrise. It is Fardh till the last minute before sunrise. After sunrise, it becomes Qadha.

‘Wassalam.

Many of our leading Maraaje' of Taqleed say that eldest sin is responsible to compensate the obligatory worship missed by his disobeying parent.

Any other son or daughter or friend or even a paid person can perform such Qadha worship in behalf of the late person.

'Wassalam.

There is no difference between the meaning of Fardh and Wajib according to majority of Sunni scholars ( Shafi'ee, Maliki, and Hanbali sects) except Abu Haneefa sect who say that Fardh is what has come as an obligatory in Quran, while Wajib is according Hanafi sect is the obligatory which came in Sunnah.

Shia Ulama have no difference in the meaning of Fardh and Wajib as both mean obligatory.

'Wassalam.